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Vlad [161]
3 years ago
6

Evaluate the given integral by changing to polar coordinates. sin(x2 + y2) dA R , where R is the region in the first quadrant be

tween the circles with center the origin and radii 2 and 3
Mathematics
1 answer:
koban [17]3 years ago
8 0

Set

\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dA=r\,\mathrm dr\,\mathrm d\theta

The region R is given in polar coordinates by the set

R=\left\{(r,\theta)\mid2\le r\le3,0\le\theta\le\dfrac\pi2\right\}

So we have

\displaystyle\iint_R\sin(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_2^3r\sin(r^2)\,\mathrm dr\,\mathrm d\theta=\boxed{\frac\pi4(\cos4-\cos9)}

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What is one way to find the total cost of jacket for $15.30 with a sales tax of 6.5%
aksik [14]

Answer:

Step-by-step explanation:

sales tax = total sales * tax rate

or I=PrT

s=(15.30)(.065)

s=.99

15.3+.99=16.29

8 0
3 years ago
Read 2 more answers
Suppose that angle COP and angle TOD are vertical angles, the measure of angle COP is 11x-17 and The measure of angle TOD is 9x+
crimeas [40]

The measure of <COD  and <POT are 43 and 43degrees respectively

The point where two lines meet or intersect is known as an angle:

Is <COP and angle TOD are vertical angles, this means that they are equal i.e.

  • <COP = <TOD

Given that:

<COP = 11x - 17

<TOD = 9x + 11

Equate both expressions

11x - 17 = 9x + 11

11x - 9x = 11 + 17

2x = 28

x = 28/2

x = 14

Get <COP

<COP = 11x - 17

<COP = 11(14) - 17

<COP = 154-17

<COP = 137 degrees

Since <COP = <TOD, hence <TOD = 137 degrees

Calculate <COD:

<COD + <TOD = 180

<COD + 137 = 180

<COD = 180 - 137

<COD  = 43 degrees

Also <POT = <COD = 43degrees(vertically opposite angles)

Hence the measure of <COD  and <POT are 43 and 43degrees respectively

Learn more here: brainly.com/question/17247176

4 0
3 years ago
8. A cable car travels 2236 m to climb a mountain that is 1000 m high. It then travels 1414 m to descend 1000 m on the other sid
frutty [35]

Answer:

3000 m

Step-by-step explanation:

Using Pythagoras theorem

2236^2=1000^2+|AB|^2\\|AB|^2=2236^2-1000^2\\|AB|^2=3999696\\|AB|=\sqrt{3999696} \\=1999.9

Similarly

1414^2=1000^2+|BC|^2\\|BC|^2=1414^2-1000^2\\|BC|^2=999696\\|BC|=\sqrt{999696} \\=999.7m

Length of the Tunnel = |AB|+|BC|

=1999.9+999.7

=2999.6

=3000 m

4 0
3 years ago
Brianna is getting materials for a chemistry experiment. Her teacher gives her a container that has 0.25 liter of a liquid in it
IgorC [24]

Answer: 0.1 liter

Step-by-step explanation:

From the question, we are informed that Brianna teacher gives her a container that has 0.25 liter of a liquid in it and she needs to use 0.4 of this liquid for the experiment.

The amount of liquid that Brianna will use will be:

= 0.4 × 0.25 liters

= 0.1 liter

6 0
3 years ago
Need the answer asap
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B I think.correct if I’m wrong
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